Madison Math Circle Abstracts: Difference between revisions

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[[Image:logo.png|right|440px|link=https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle]]
[[Image:logo.png|right|440px|link=https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle]]


== August 6 2016  ==
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle Main Math Circle Page]
 
 
 
== September 18 2017 ==
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Science Saturday'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Daniel Erman'''
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| bgcolor="#BDBDBD"  align="center" | '''Title: Game Busters'''
| bgcolor="#BDBDBD"  align="center" | '''Title: Welcome to the Madison Math Circle!'''
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The goal of our station will be to explore the mathematics related to the games: Set, Nim, and Chomp. We will have stations where individuals can drop by play a few games and explore these games for themselves. (We will have worksheets and volunteers providing guidance.) Additionally, anyone will be able to challenge our Master of Nim with fun prizes available for beating them. (Note: This is at a special time and location.)
Abstract:  At the Madison Math Circle, we aim to give a flavor for the creative type of thinking that goes into mathematical research. In this week's interactive activity, students will explore questions related to Mobius strips, developing their own conjectures.
<ul>
<li> [https://www.math.wisc.edu/wiki/images/Chomp_Sol.pdf Solutions for Chomp] </li>
<li> [https://www.math.wisc.edu/wiki/images/Nim_sol.pdf Solutions for Nim] </li>
<li> [https://www.math.wisc.edu/wiki/images/Set_sol.pdf Solutions for Set].</li>
</ul>
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== September 12 2016 ==
== September 25 2017 ==
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Jean-Luc Thiffeault'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Betsy Stovall'''
|-
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| bgcolor="#BDBDBD"  align="center" | '''Title: Why do my earbuds keep getting entangled?'''
| bgcolor="#BDBDBD"  align="center" | '''Title: Math is a game!'''
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I'll discuss the mathematics of random entanglements.  Why is it that
When mathematicians are working to solve a theoretical problem, it often helps to imagine that we are playing a game:  What could our opponent do to make our job as difficult as possible, and what is our strategy to defeat them no matter what move they make?  In this session, we will try this out by playing several games and trying to come up with winning strategies. 
it's so easy for wires to get entangled, but so hard for them to
detangle?
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== September 19 2016 ==
== October 2 2017 ==
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Rachel Davis'''
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| bgcolor="#BDBDBD"  align="center" | '''Title: Is Any Knot Not the Unknot?'''
| bgcolor="#BDBDBD"  align="center" | '''Title: Thinking outside the box'''
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You're walking home from school, and you pull out your head phones to listen to some tunes. However, inevitably they are a horribly tangled mess, but are they really a knot? We'll talk about what exactly is a knot, and how we can tell when something is not the unknot.
Abstract: We will try some geometric puzzles related to area, volume, and dimension using techniques such as drawing diagrams, looking at special cases, using symmetry, and changing perspective.
 
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== September 26 2016 ==
== October 9 2017 ==
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Megan Maguire'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Solly Parenti'''
|-
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| bgcolor="#BDBDBD"  align="center" | '''Title: Coloring Maps'''
| bgcolor="#BDBDBD"  align="center" | '''Title: Hackenbush'''
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Have you ever noticed that in colored maps of the US bordering states are never the same color? That's because it would be super confusing! But how many different colors do we need in order to avoid this? Come find out and learn more cool things about coloring maps.
Abstract: I come from an alien world where we spend all of our time playing a game called hackenbush.  I'd like to introduce y'all to this game so you don't embarass yourself if you come visit my planet.
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== October 3 2016 ==
== October 16 2017 ==
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Zach Charles'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Mihaela Ifrim'''
|-
|-
| bgcolor="#BDBDBD"  align="center" | '''Title: 1 + 1 = 10, or How does my smartphone do anything?'''
| bgcolor="#BDBDBD"  align="center" | '''Title: Escape of the Clones!'''
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Computers are used to do all kinds of complex tasks, from playing videos to running internet browsers. Secretly, computers do everything through numbers and mathematics. Surprisingly, they do all of this with "bits", numbers that are only 0 or 1. We will talk about bits and how we use them to do the mathematics we're familiar with as humans. If we have enough time, we will discuss "addition chains" and how computers use them to speed up their computations.
Abstract: We wish to find an invariant (an invariant is a quantity that doesn't change no matter how the process plays out). By playing couple of games will help us find some! The main game we will play is Escape of the Clones! Promise you will like it!
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== October 10 2016 ==
== October 23 2017 ==
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Keith Rush'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker'''
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| bgcolor="#BDBDBD"  align="center" | '''Title: Randomness, determinism and approximation: a historical question'''
| bgcolor="#BDBDBD"  align="center" | '''Title: TBD'''
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If you give me a function, can I find a simple function that approximates it well? This question played a central role in the development of mathematics. With a couple examples we will begin to investigate this for ourselves, and we'll touch on some interesting relationships to modeling random processes.
Abstract
 
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== October 17 2016 ==
== October 30 2017 ==
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Philip Wood'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker'''
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| bgcolor="#BDBDBD"  align="center" | '''Title: The game of Criss-Cross'''
| bgcolor="#BDBDBD"  align="center" | '''Title: TBD'''
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Some say that mathematics is the science of patterns, and patterns are everywhere.  You can find some remarkable patterns just by drawing lines connecting dots, and that is just what we will do in the game of Criss-Cross!  Bring your pencils and be ready to play.
Abstract
 
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== October 24 2016 ==
== November 6 2017 ==
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Ethan Beihl'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker'''
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| bgcolor="#BDBDBD"  align="center" | '''Title: A Chocolate Bar for Every Real Number'''
| bgcolor="#BDBDBD"  align="center" | '''Title: TBD'''
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By chopping up rectangles into squares repeatedly we obtain so-called "slicing diagrams" that correspond to every number. These diagrams have some very cool properties, and show up all over mathematics (under the name "continued fractions," which name we will investigate). Some questions I may ask you: Which chocolate bars look like themselves? Which chocolate bars look like themselves, except bigger? Which chocolate bars are interesting? Why did you come to a math talk expecting real chocolate?
Abstract
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== October 31 2016 ==
== November 13 2017 ==
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''No Meeting This Week'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker'''
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| bgcolor="#BDBDBD"  align="center" | '''Title: N/A'''
| bgcolor="#BDBDBD"  align="center" | '''Title: TBD'''
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Abstract
Enjoy Halloween.
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== November 7 2016 ==
 
 
== November 20 2017 ==
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Polly Yu'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker'''
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| bgcolor="#BDBDBD"  align="center" | '''Title: Are we there yet?'''
| bgcolor="#BDBDBD"  align="center" | '''Title: TBD'''
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Abstract
When you are told to clean your room, you have to first clean half of it; then half of what's left, and half of what's left, and so on. Seems like you will never be done! In fact, an ancient Greek philosopher, Zeno, used an argument like this to claim that it is impossible to move! Disclaimer: we are not saying that it's impossible to clean your room. What we will do is look at a special case of adding infinitely many numbers together, and use the resulting formula to calculate areas of fractals.
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== November 14 2016 ==
== January 29 2018 ==
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Micky Soule Steinberg'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker'''
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| bgcolor="#BDBDBD"  align="center" | '''Title: Circles and Triangles'''
| bgcolor="#BDBDBD"  align="center" | '''Title: TBD'''
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Abstract
We’ll talk about the pythagorean theorem and areas of circles/triangles, and then use those tools to solve some cool problems!
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== November 21 2016 ==
== February 5 2018 ==
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<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Benedek Valko'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker'''
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| bgcolor="#BDBDBD"  align="center" | '''Title: Fun with hats'''
| bgcolor="#BDBDBD"  align="center" | '''Title: TBD'''
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Abstract
We will discuss various fun logic problems involving colors of hats. The participants will also have a chance to win some of the speaker’s leftover Halloween candy.
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== February 12 2018 ==
== February 6 2017 ==
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<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Cullen McDonald'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker'''
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| bgcolor="#BDBDBD"  align="center" | '''Title: Building a 4-dimensional house'''
| bgcolor="#BDBDBD"  align="center" | '''Title: TBD'''
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Abstract
I think my dream home would be in the fourth dimension. I'd have a lot more room for activities. We will draw blueprints, build models, and measure how much more room we'll get by using mathematics to extend our understanding of 3 dimensions to 4 or beyond.
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== February 13 2017 ==
== February 19 2018 ==
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<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Dima Arinkin'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker'''
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| bgcolor="#BDBDBD"  align="center" | '''Title: Solve it with colors'''
| bgcolor="#BDBDBD"  align="center" | '''Title: TBD'''
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Abstract
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</center>


How many ways are there to place 32 dominoes on a 8x8 chessboard? (Dominoes cover exactly two squares, and should not overlap.) This is a very tough problem with a huge answer: 12,988,816. But suppose we want to only place 31 dominoes and leave two opposite corners empty. It turns out that the question is then almost trivial: such a placement is impossible. (Hint: The reason has to do with black and white squares on the board!)
== February 26 2018 ==
We will look at problems that can be solved by a clever coloring design.
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= High School Meetings =
== October 17 2016 (JMM) ==
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Daniel Erman'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker'''
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| bgcolor="#BDBDBD"  align="center" | '''Title: What does math research look like?'''
| bgcolor="#BDBDBD"  align="center" | '''Title: TBD'''
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Using a concrete problem in combinatorics, I will try to give a feel for what math research looks like.  We’ll discuss the various aspects of research including:  gathering data, making conjectures, proving special cases, and asking new questions.
Abstract
 
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== October 24 2016 (West) ==
== March 5 2018 ==
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<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
|-
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker'''
|-
|-
| bgcolor="#BDBDBD"  align="center" | '''Title: Shhh, This Message is Secret'''
| bgcolor="#BDBDBD"  align="center" | '''Title: TBD'''
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|-
| bgcolor="#BDBDBD"  |   
| bgcolor="#BDBDBD"  |   
gur pbearefgbar bs gur zbqrea jbeyq eribyirf nebhaq orvat noyr gb rnfvyl pbzzhavpngr frpergf, jurgure gubfr frpergf or perqvg pneq ahzoref ba nznmba, grkg zrffntrf ba lbhe vcubar, be frpher tbireazrag nssnvef. va guvf gnyx jr jvyy rkcyber gur zngu haqrecvaavat bhe novyvgl gb qb guvf, naq frr whfg ubj fgheql gung pbearefgbar npghnyyl znl or.
Abstract
 
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== October 31 2016 (East)==
== March 12 2018 ==
<center>
<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
|-
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker'''
|-
|-
| bgcolor="#BDBDBD"  align="center" | '''Title: Shhh, This Message Is Secret'''
| bgcolor="#BDBDBD"  align="center" | '''Title: TBD'''
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|-
| bgcolor="#BDBDBD"  |   
| bgcolor="#BDBDBD"  |   
gur pbearefgbar bs gur zbqrea jbeyq eribyirf nebhaq orvat noyr gb rnfvyl pbzzhavpngr frpergf, jurgure gubfr frpergf or perqvg pneq ahzoref ba nznmba, grkg zrffntrf ba lbhe vcubar, be frpher tbireazrag nssnvef. va guvf gnyx jr jvyy rkcyber gur zngu haqrecvaavat bhe novyvgl gb qb guvf, naq frr whfg ubj fgheql gung pbearefgbar npghnyyl znl or.
Abstract
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== December 5 2016 (JMM) ==
== March 19 2018 ==
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<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
|-
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Philip Matchett Wood'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker'''
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|-
| bgcolor="#BDBDBD"  align="center" | '''Title: The game of Criss-Cross'''
| bgcolor="#BDBDBD"  align="center" | '''Title: TBD'''
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|-
| bgcolor="#BDBDBD"  |   
| bgcolor="#BDBDBD"  |   
Some say that mathematics is the science of patterns, and patterns are everywhere.  You can find some remarkable patterns just by drawing lines connecting dots, and that is just what we will do in the game of Criss-Cross!  Bring your pencils and be ready to play.
Abstract
 
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== December 5 2016 (East) ==
== April 2 2018 ==
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<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Uri Andrews'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker'''
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|-
| bgcolor="#BDBDBD"  align="center" | '''Title: How to split an apartment'''
| bgcolor="#BDBDBD"  align="center" | '''Title: TBD'''
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|-
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So you go off to college and after a year or two, you and some of your friends decide to get an apartment together. It'll be a lot of fun living with your best friends. Then move-in day comes, and you realize that everyone wants the room by the kitchen (for easy late-night snacking). You have 4 rooms and 4 people. Surely there must be some way to make everybody happy. People are willing to settle for their second-favorite room instead if maybe they pay a little less rent or do some less chores. How do you navigate this issue to make everybody happy? I'll share a way to do this based on a mathematical theorem which also explains the following fact: If you stir up a cup of hot chocolate, when the liquid has come to rest, some point in the liquid will end up in exactly the same place in the cup as before you stirred it.
Abstract
 
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== February 13 2017 (East) ==
== April 9 2018 ==
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Eva Elduque'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker'''
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| bgcolor="#BDBDBD"  align="center" | '''Title: Pick's Theorem'''
| bgcolor="#BDBDBD"  align="center" | '''Title: TBD'''
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In this talk, we will work to discover a beautiful formula that allows us to quickly and easily compute the area of a polygon whose vertices are points of a grid. We will prove that this formula works!
Abstract
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== February 20 2017 (JMM) ==
 
= Off-Site Meetings =
== October 2 2017 (East High School) ==
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Megan Maguire'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker TBD'''
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| bgcolor="#BDBDBD"  align="center" | '''Title:  Coloring Maps'''
| bgcolor="#BDBDBD"  align="center" | '''Title:  How to make it as a Hackenbush player in the planet Zubenelgenubi 4'''
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Have you ever noticed that in colored maps of the US bordering states are never the same color? That's because it would be super confusing! But how many different colors do we need in order to avoid this? Come find out and learn more cool things about coloring maps.
Abstract: In the distant planet of Zubenelgenubi 4, we live our life without numbers. I know, how do we pass our time if we can't construct a smartphone without numbers? The answer is that we have invented an extremely violent sport about chopping down trees called Hackenbush, and playing this game is an essential social skill in Zubenelgenubi 4. I will teach you how to play the pen and paper version of Hackenbush, and hint at how learning this game leads to a kind of math that is highly illegal in 254,233 planetary systems.
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Revision as of 02:51, 16 October 2017

Logo.png

Main Math Circle Page


September 18 2017

Daniel Erman
Title: Welcome to the Madison Math Circle!

Abstract: At the Madison Math Circle, we aim to give a flavor for the creative type of thinking that goes into mathematical research. In this week's interactive activity, students will explore questions related to Mobius strips, developing their own conjectures.

September 25 2017

Betsy Stovall
Title: Math is a game!

When mathematicians are working to solve a theoretical problem, it often helps to imagine that we are playing a game: What could our opponent do to make our job as difficult as possible, and what is our strategy to defeat them no matter what move they make? In this session, we will try this out by playing several games and trying to come up with winning strategies.

October 2 2017

Rachel Davis
Title: Thinking outside the box

Abstract: We will try some geometric puzzles related to area, volume, and dimension using techniques such as drawing diagrams, looking at special cases, using symmetry, and changing perspective.

October 9 2017

Solly Parenti
Title: Hackenbush

Abstract: I come from an alien world where we spend all of our time playing a game called hackenbush. I'd like to introduce y'all to this game so you don't embarass yourself if you come visit my planet.

October 16 2017

Mihaela Ifrim
Title: Escape of the Clones!

Abstract: We wish to find an invariant (an invariant is a quantity that doesn't change no matter how the process plays out). By playing couple of games will help us find some! The main game we will play is Escape of the Clones! Promise you will like it!

October 23 2017

Speaker
Title: TBD

Abstract

October 30 2017

Speaker
Title: TBD

Abstract

November 6 2017

Speaker
Title: TBD

Abstract

November 13 2017

Speaker
Title: TBD

Abstract


November 20 2017

Speaker
Title: TBD

Abstract

January 29 2018

Speaker
Title: TBD

Abstract

February 5 2018

Speaker
Title: TBD

Abstract

February 12 2018

Speaker
Title: TBD

Abstract

February 19 2018

Speaker
Title: TBD

Abstract

February 26 2018

Speaker
Title: TBD

Abstract

March 5 2018

Speaker
Title: TBD

Abstract

March 12 2018

Speaker
Title: TBD

Abstract

March 19 2018

Speaker
Title: TBD

Abstract

April 2 2018

Speaker
Title: TBD

Abstract

April 9 2018

Speaker
Title: TBD

Abstract


Off-Site Meetings

October 2 2017 (East High School)

Speaker TBD
Title: How to make it as a Hackenbush player in the planet Zubenelgenubi 4

Abstract: In the distant planet of Zubenelgenubi 4, we live our life without numbers. I know, how do we pass our time if we can't construct a smartphone without numbers? The answer is that we have invented an extremely violent sport about chopping down trees called Hackenbush, and playing this game is an essential social skill in Zubenelgenubi 4. I will teach you how to play the pen and paper version of Hackenbush, and hint at how learning this game leads to a kind of math that is highly illegal in 254,233 planetary systems.